Washington (CNN) -- Behind-the-scenes dealing over reviving stalled gun control legislation will get a push next week when Sen. Joe Manchin, a strong proponent of expanding background checks, plans to meet individually with lawmakers, a Senate source tells CNN.
The key question the conservative West Virginia Democrat wants answered is whether a "minimal change" to a compromise background check proposal that he co-authored but which failed to gain enough support in a vote last month would entice more senators to support it, the source said.
Since the proposal he negotiated with Republican Sen. Pat Toomey of Pennsylvania faltered, senators who voted against it have been hounded in their states during the current recess by outside proponents of expanding background checks.
Sen. Kelly Ayotte has been the most high-profile target of such confrontations. The New Hampshire Republican was questioned at an event by Erica Lafferty, the daughter of Dawn Hochsprung, a school principal slain in the Newtown massacre last December.
Lafferty asked "why the burden of my mother being gunned down in the halls of her elementary school isn't as important" as inconveniencing gun sellers.
Lafferty was sent to Ayotte's event by Mayors Against Illegal Guns, one of several gun control groups using the current congressional recess to take the gun control message out of Washington. And she followed that up with interviews with TV networks.
The source said this sort of pressure from outside groups is a key to any hopes of swaying senators who may be open to supporting a modified proposal.
In addition to confronting senators in person, groups have run ads against lawmakers who voted against the Toomey-Manchin compromise and have supported senators who supported it.
The husband of former Rep. Gabrielle Giffords, who was seriously wounded in a 2011 shooting in Arizona, wrote an opinion piece in the Houston Chronicle challenging the National Rifle Association over its opposition to expanded background checks.
"What most members of the NRA want from the organization and what the leadership is actually doing are not the same," Mark Kelly wrote.
Thousands of NRA members are gathered in Houston this weekend for its annual convention.
According to the Senate source, the pressure tactics appear to be working with polls showing most Americans favoring some sort of new gun restrictions.
The signal Manchin has been getting from senators getting hammered at home, according to the source, is that they need to save face politically and any deal would hinge on whether they can argue that they extracted something new in the language.
"We have to figure out some sort of new sentence, one change to it so they can go back and say 'I fought to change this,'" said the source.
At this point, however, it is not clear what the change would be.
In order to pass any legislation around the issue, gun control advocates need find 60 votes in the Senate. Fifty-four senators backed the Mancin-Toomey amendment while 46 opposed it. Majority Leader Harry Reid supported it but only voted 'no' in the end on procedural grounds to keep open the possibility of revisiting it later.
The Senate source says Manchin's prime targets to flip are all Republicans and similar to those under pressure from outside groups: Ayotte, Sen. Jeff Flake of Arizona, Sen. Lisa Murkowski of Alaska and Sen. Dean Heller of Nevada.
According to the source, proponents hope that if Murkowski flips, those in favor of tightening gun laws will have a good shot at getting her fellow Alaskan, Sen. Mark Begich, to do the same. But a source close to Begich, however, told CNN that it is very unlikely that he'd change his vote.
He is up for reelection in 2014 in a state that is very pro-gun.
The NRA is likely to be a power that looms large over any deal on background checks, much like it was during the last debate.
After the compromise background check proposal failed, the NRA Institute for Legislative Action released a statement decrying the "misguided" amendment that, it said, would "not reduce violent crime or keep our kids safe in their schools."
"This amendment would have criminalized certain private transfers of firearms between honest citizens, requiring lifelong friends, neighbors and some family members to get federal government permission to exercise a fundamental right or face prosecution," the NRA said.
Wayne LaPierre, executive vice president of the NRA, made it clear on Friday that his organization would not budge on guns.
"All over this country, everywhere I go, people agree, they want bad guys taken off the streets and they want children protected in their schools," he said. "And they don't' want their freedom taken away."
In addition to LaPierre, several potential contenders for the 2016 GOP nomination will take the stage in Houston, including Sen. Ted Cruz of Texas, Louisiana Gov. Bobby Jindal, Texas Gov. Rick Perry, former Sen. Rick Santorum of Pennsylvania, and Wisconsin Gov. Scott Walker. Former vice presidential nominee Sarah Palin spoke to the group as well.
Republican Sen. John McCain of Arizona, asked by one of the other victims of the Giffords shooting if he thought background checks would come up again, said there was a "50-50" chance that it would.
A spokeswoman for Democratic Sen. Max Baucus of Montana, one of the more high-profile Democrats to vote against the provision, told CNN that if such a bill were to come up, "Max will evaluate it based on the feedback he gathers from the people of Montana, just as he always does with any legislation."
But she also said that in his first vote, "Montanans told Max loud and clear they didn't support new gun controls in the previous bill."
CNN's Kevin Liptak and Ashley Killough contributed to this report